Also not possible in Turkey, but at least this service works.
Having said that, I don't think the market for painless cancelling is big enough to do this given the legal overhead that would be needed.
At this point, everything continues as if this system wasn't involved, but now you have proof of intent to cancel. If they don't act on it in 2 work days you are in no obligation to pay for them anymore. And even if you accidentally do pay, you will be refunded.
Has any of the code and infrastructure been open sourced?
And, there's no real incentive to improve, while with private companies, if you don't like them, you just stop paying for them. That profit motive (and threat of its loss) is very powerful - much more powerful than the "I'm helping my fellow citizen by engaging in civil service" (or, perhaps more likely, "I'm accruing power by running for public office").
That's why this "click to cancel" proposal is so important: it keeps companies from becoming embedded, like the incumbent govt that gets lazy and complacent, knowing that they'll never get voted out.
Hard, because the government has authority, a random company does not.
I'd still trust my government more than a random non profit company, if my trust decreases, I'd vote for different people to manage the country - which is not possible with companies.